A164687 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

1, 43, 1806, 75852, 3185784, 133802928, 5619722976, 236028364089, 9913191253812, 416354031068115, 17486869237997292, 734448505187617668, 30846837099932661024, 1295567153243385959664, 54413820228163207379946

Offset

0,2

Comments

The initial terms coincide with those of A170762, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

Links

Table of n, a(n) for n=0..14.

Index entries for linear recurrences with constant coefficients, signature (41, 41, 41, 41, 41, 41, -861).

Formula

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(861*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).

Mathematica

coxG[{7, 861, -41}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 30 2016 *)

Crossrefs

Sequence in context: A163226 A163745 A164113 * A165175 A165694 A166233

Adjacent sequences: A164684 A164685 A164686 * A164688 A164689 A164690

Keyword

nonn

Author

John Cannon and N. J. A. Sloane, Dec 03 2009

Status

approved